ИСТИНА

On a fixed time interval we consider the control system of Volterra type integral equations. Among its solutions satisfying endpoint constraints, state and mixed constraints, one should minimize an endpoint cost functional. We assume that the mixed constraints are regular, i.e. their gradients with respect to $u$ of all active inequality constraints and all equality constraints are positively--linearly independent. Necessary conditions for a weak minimum are obtained that generalize the Euler--Lagrange equation for problems with ODEs.